非歐幾何的發(fā)展史及其啟示

摘 要

在數(shù)學史上,非歐幾何占有特殊的地位.人們常將非歐幾何引起的變革與哥白尼的革命相比擬.本文以非歐幾何的發(fā)明過程為基本線索，探討其對對數(shù)學學科本身、人類文化、哲學思想的影響；也研究了其對數(shù)學科研者、數(shù)學教育者、中學生、高校學生的啟示。
關(guān)鍵詞：非歐幾何；羅巴切夫斯基幾何；黎曼幾何；啟示

The history of non-Euclidean geometry and the development of its revelation

Abstract

The non-Euclidean geometry holds the special status in the history of mathematics. People usually compare the revolution of Copernicus with the transformation of Non-Euclidean geometry. This article take the non-Euclidean geometry invention process as the basic clue, has discussed the impact of the mathematical Science itself ，humanity culture and the philosophy thought；also studied its revelation to mathematics researchers, mathematics teachers， the middle-school students and the university students.     
Key words：Non-Euclidean geometry；Lobatchevskian geometry；Riemannian geometry；revelation；

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